[PPT] - TMD phenomenology and A N in pp collisions Umberto DAlesio Physics PowerPoint Presentation

SLIDE 1

TMD phenomenology and AN in pp collisions

Umberto D’Alesio Physics Department & INFN University of Cagliari, Italy Workshop on Opportunities for Polarized Physics at FERMILAB based on work in collaboration with

M. Anselmino, M. Boglione, E. Leader, S. Melis, F. Murgia, C. Pisano and A. Prokudin

SLIDE 2

U. D’Alesio

Fermilab - 21 May 2013

Outline

AN in pp → hX

– experimental status – theoretical approaches: Twist-3 vs. TMD approach

TMD approach: Collins vs. Sivers effect in pp → h X
Access to the Sivers effect: pp → jet X and pp → γ X
Access to the Collins effect: pp → jet πX
AN at midrapidity and the gluon Sivers function
Conclusions

TMD phenomenology and AN in pp collisions 1

SLIDE 3

U. D’Alesio

Fermilab - 21 May 2013

SSAs in p↑p → h X

AN ≡ dσ↑−dσ↓

dσ↑+dσ↓ still challenging

xF = 2pL/√s started long time ago

0.6
0.4
0.2

0.2 0.4 0.6 0.2 0.4 0.6 0.8 1

xF AN

π+ π0 π−

√s = 20 GeV [E704 coll. 91]

TMD phenomenology and AN in pp collisions 2

SLIDE 4

U. D’Alesio

Fermilab - 21 May 2013

SSAs in p↑p → h X

AN ≡ dσ↑−dσ↓

dσ↑+dσ↓ still challenging

xF = 2pL/√s confirmed at much larger energies √s = 200 GeV [STAR coll. 08]

TMD phenomenology and AN in pp collisions 3

SLIDE 5

U. D’Alesio

Fermilab - 21 May 2013

SSAs in p↑p → h X

AN ≡ dσ↑−dσ↓

dσ↑+dσ↓ still challenging

xF = 2pL/√s and at even larger energies and at large PT

0.05 0.1 2 3 4 5 6 7 8 AN PT (GeV) STAR preliminary xF = 0.20 70 mrad 30 mrad 0.05 0.1 2 3 4 5 6 7 8 AN PT (GeV) STAR preliminary xF = 0.28 70 mrad 30 mrad

√s = 500 GeV [STAR coll. 12] [Preliminary]

TMD phenomenology and AN in pp collisions 4

SLIDE 6

U. D’Alesio

Fermilab - 21 May 2013

AN: sizeable at large rapidity, increasing with xF and PT (RHIC)
Theoretical approaches
1. collinear pQCD factorization at twist-3:

universal quark-gluon-quark correlators, (i.e. TF(x, x)) [Efremov-Teryaev 82,85; Qiu-Sterman 91,92,98; Kouvaris et al. 06; Kanazawa- Koike 00,10; Kang et al. 11]

2. Generalized Parton Model (GPM): TMD effects (assuming factorization)

[Anselmino-Boglione-Murgia 95, Anselmino et al. 06; UD-Murgia 04,08; Anselmino et al. 12,13]

TMD phenomenology and AN in pp collisions 5

SLIDE 7

U. D’Alesio

Fermilab - 21 May 2013

Motivations: phenom. point of view

pp → h X

– suppression of the Collins effect REVISITED! – use of phenomenological information gathered from SIDIS and e+e− data potential role of Collins and Sivers effects in AN in pp → π X – sign mismatch issue Twist-3 qgq-correlation funct. from SIDIS Sivers funct.: wrong sign in AN

other final states (jet, γ, pion-jet)

– disentangling Collins and Sivers effects and approaches – study of universality-breaking effects

AN at mid-rapidity: role, if any, of the gluon Sivers function

TMD phenomenology and AN in pp collisions 6

SLIDE 8

U. D’Alesio

Fermilab - 21 May 2013

Twist-3 approach

Three contributions to AN (schematic view) large xF Φ(3)

q/p↑⊗ fq/p

⊗ σ ⊗ Dh/q

able [⋆] to describe AN (FIT) [Kouvaris et al. 06]

∆Tq ⊗ Φ(3)

q↑/p ⊗ σ′ ⊗ Dh/q

negligible [Kanazawa-Koike 00]

∆Tq ⊗ fq/p ⊗ σ′′ ⊗ D(3)

h/q↑ ? under study [Kang-Yuan-Zhou 10, Metz-Pitonyak 12]

Notice:

Φ(3)

q/p↑ → TF(x, x) Efremov-Teryaev-Qiu-Sterman correlation function

⋆ Correction of an overall sign in the definition of gTF [Kang et al. 11]

TMD phenomenology and AN in pp collisions 7

SLIDE 9

U. D’Alesio

Fermilab - 21 May 2013

The sign mismatch issue

Link between Sivers and ETQS functions [Boer-Mulders-Piljman 03] ∫ d2k⊥ (k2

⊥

M ) f ⊥q

1T (x, k2 ⊥)|SIDIS = −g TF(x, x)

⋆ sign mismatch in AN (if only TF!) [Kang et al. 11]

0.1
0.05

0.05 0.1 0.2 0.4 0.6 0.8 1 Q=2 GeV u-quark x x gTu,F(x, x)

TF from pp vs. TF via f ⊥

1T

Solutions:

node in x [Kang-Prokudin 12] and/or in k⊥ (likely ruled out)
TMD evolution and k⊥ spreading
study of AN in lp → l′X via qγq ⇐

⇒ qgq correlators [Metz et al. 12]

additional and LARGE twist-3 effects (fragmentation sector)?

[Metz-Pitonyak 12] still an open an intriguing issue!

TMD phenomenology and AN in pp collisions 8

SLIDE 10

U. D’Alesio

Fermilab - 21 May 2013

TMD approach

Many contributions from nonplanar partonic kinematics (helicity formalism) [Anselmino et al. 06] ∆Nfq/p↑ ⊗ fq/p ⊗ σ ⊗ D cos φq Sivers funct. (f ⊥

1T)

∆Tq ⊗ ∆Nfq↑/p ⊗ σ′ ⊗ Dh/q cos ψ′ Boer-Mulders funct. (h⊥

1 )

∆Tq ⊗ fq/p ⊗ σ′′ ⊗ ∆NDh/q↑ cos ψ′′ Collins funct. (H⊥

1 )

plus others and plus contributions from gluon TMDs ⊗: convolutions on x, k⊥; ψ’s complicate calculable azimuthal phases Only Sivers and Collins effects survive under integration over angular depend.s Let’s consider separately the Collins and Sivers effects

TMD phenomenology and AN in pp collisions 9

SLIDE 11

U. D’Alesio

Fermilab - 21 May 2013

Collins effect (revisited)

riginal claimed suppression due
to wrong sign in the spin transfer for qg → qg: one of the most important channels
to relative cancelation with other channels: qq → qq and q¯

q → q¯ q. Role of intrinsic azimuthal phases: relevant but not totally suppressing ⇒ a new realistic reanalysis [Anselmino-Boglione-UD-Leader-Melis-Murgia-Prokudin 12]

TMD phenomenology and AN in pp collisions 10

SLIDE 12

U. D’Alesio

Fermilab - 21 May 2013

Phenomenology of the Collins effect

use of available information on the Collins effect from SIDIS and e+e− data
global fit not worth at this stage (non separable effects in pp)
universality of the Collins function

[Collins-Metz 04, Yuan 08]

∆Tq not constrained at large x (SIDIS data x ≤ 0.3) impact on AN at large xF

d(x)

T

∆ x u(x)

T

∆ x

x

−0.1 0.1 0.2 0.3 0.4 0.5

0.2 0.4 0.6 0.8 1 −0.2 −0.15 −0.1 −0.05 0.05 0.1

Present status - large errors large x behaviour ≃ (1 − x)β with

1. β =4.74±5.45 [Anselmino et al. 07]
2. β =0.84±2.30 [Anselmino et al. 09] ⇐
3. β =3.64+5.80

−3.37

[Anselmino et al. 13]

TMD phenomenology and AN in pp collisions 11

SLIDE 13

U. D’Alesio

Fermilab - 21 May 2013

Large-x behaviour of the transversity ∆Tq(x, k⊥) ≃ N T

q xαq (1 − x)βq [q(x) + ∆q(x)]

2 g(k⊥) q = u, d

use of isospin symmetry + only favoured and disfavoured FFs
flavour independent parameters except βq
proper evolution for ∆Tq, DGLAP for ∆ND
9 parameters to be fitted: ... βu, βd ...

TMD phenomenology and AN in pp collisions 12

SLIDE 14

U. D’Alesio

Fermilab - 21 May 2013

Scan Procedure

I step

1. 9-parameter reference fit on SIDIS (HERMES, COMPASS) and e+e− (Belle) data
2. grid (scan) of the parameters, βu, βd within the range (0.0–4.0)
3. 7-parameter fit to SIDIS and e+e− data adopting the βq-grid
4. selection via χ2

scan ≤ χ2 min + ∆χ2|ref.fit (stat. uncert. band) [fulfilled by all fits]

5. computation of Collins pion SSA for pp collisions

)

h

φ +

S

φ sin ( UT

A

x

0.05 0.1 0.15 0.2 0.25 0.3 0.35 −0.05 0.05 0.1

HERMES X

+

π l →

↑

lP = 7.25374 (GeV) s

example of the fit with β fixed: scan band on HERMES π+ data

TMD phenomenology and AN in pp collisions 13

SLIDE 15

U. D’Alesio

Fermilab - 21 May 2013

Results

Collins contribution Envelope curves (scan band)

0.2
0.1

0.1 0.2 0.2 0.3 0.4 AN xF θ = 2.3° π+ π− 0.1 0.2 0.3 0.4 xF θ = 4.0°

0.05

0.05 0.1 0.15 0.2 0.4 0.6 AN xF η = 3.3 π0 0.2 0.4 0.6 xF η = 3.7

BRAHMS@RHIC 2007 √s = 200 GeV STAR@RHIC 2008 able to describe AN for charged pions, but not the large-xF neutral pion SSA data

TMD phenomenology and AN in pp collisions 14

SLIDE 16

U. D’Alesio

Fermilab - 21 May 2013

II step: further tests

1. best curve within the scan and computation of its statistical error band (π0-STAR)
2. allowance for full flavour dependence and back to step I (13-parameter fit)
3. also tried: a transversity-like evolution for the Collins function (not relevant)

TMD phenomenology and AN in pp collisions 15

SLIDE 17

U. D’Alesio

Fermilab - 21 May 2013

Statistical uncertainty bands

Collins contribution

0.05

0.05 0.1 0.15 0.2 0.4 0.6 AN xF η= 3.3 π0 0.2 0.4 0.6 xF η= 3.7

0.05

0.05 0.1 0.15 0.2 0.4 0.6 AN xF η= 3.3 π0 0.2 0.4 0.6 xF η= 3.7

flavour-independent par. free parameters ∄ a single curve good at low and large xF Same conclusions for E704 data at √s = 20 GeV

TMD phenomenology and AN in pp collisions 16

SLIDE 18

U. D’Alesio

Fermilab - 21 May 2013

Collins effect: conclusions

The Collins effect, corrected, is sizeable
1. able to reproduce the low xF RHIC data.
2. not sufficient at large xF, where AN increases
Additional mechanisms are required: the Sivers effect?

Let’s consider it along the same lines

TMD phenomenology and AN in pp collisions 17

SLIDE 19

U. D’Alesio

Fermilab - 21 May 2013

Phenomenology of the Sivers effect

universality and TMD evolution of the Sivers function...open issues

– no proof of a TMD factorization for pp → hX – its twist-3 counterpart gives sizeable AN but wrong in sign – including Initial-final interactions results into a “wrong” sign [Gamberg-Kang 11] – ansatz...same Sivers functions as in SIDIS

use of available information on the Sivers effect from SIDIS data

– ∆Nfq/p↑ not constrained at x ≥ 0.3 (SIDIS) → impact on AN at large xF – large-x behaviour ≃ (1 − x)β with

1. β =0.53±3.58 [Anselmino et al. 07]
2. β =3.46+4.87

−2.90

[Anselmino et al. 09] A preliminary study based on fit (1) gave very encouraging results in pp → πX [Boglione-UD-Murgia 08]

TMD phenomenology and AN in pp collisions 18

SLIDE 20

U. D’Alesio

Fermilab - 21 May 2013

Again, explore the large-x behaviour of the Sivers function ∆Nfq/p↑(x, k⊥) ≃ 2N S

q xαq (1 − x)βq fq/p(x, k⊥) h(k⊥/M)

DGLAP evolution for ∆Nf [TMD ansatz]
focus on the valence region: sea Sivers functions set to zero

7 parameters to be fitted: ... βu, βd ...

TMD phenomenology and AN in pp collisions 19

SLIDE 21

U. D’Alesio

Fermilab - 21 May 2013

Scan Procedure

1. 7-parameter reference fit on SIDIS (HERMES, COMPASS) data
2. grid (scan) of the parameters, βu, βd within the range (0.0–4.0)
3. 5-parameter fit to SIDIS data adopting the βq-grid
4. selection via χ2

scan ≤ χ2 min + ∆χ2|ref.fit (stat. uncert. band) [fulfilled by all fits]

5. computation of Sivers SSA for pp collisions

[Anselmino-Boglione-UD-Melis-Murgia-Prokudin 13]

TMD phenomenology and AN in pp collisions 20

SLIDE 22

U. D’Alesio

Fermilab - 21 May 2013

Results

Sivers contribution

0.2
0.1

0.1 0.2 0.2 0.3 0.4 AN xF θ = 2.3° π+ π− 0.1 0.2 0.3 0.4 xF θ = 4.0°

0.05

0.05 0.1 0.15 0.2 0.4 0.6 AN xF η = 3.3 π0 0.2 0.4 0.6 xF η = 3.7

BRAHMS@RHIC 2007 √s = 200 GeV STAR@RHIC 2008 Envelope curves (scan band) able to describe AN for charged pions, as well as the large-xF neutral pion SSA data

TMD phenomenology and AN in pp collisions 21

SLIDE 23

U. D’Alesio

Fermilab - 21 May 2013

I remark about Collins vs. Sivers effect in SSAs for neutral pion production

the Collins effect suffers from 2 possible cancellations:
1. opposite sign between u and d quark transversity distributions
2. opposite sign between fav. and disfav. Collins FFs [π0 = (π+ + π−)/2]
the Sivers effect suffers only 1 possible cancellation:
1. opposite sign between u and d flavours in the distribution sector

II remark

full understanding:
verall fit of SIDIS, e+e− and AN data with Collins and Sivers effects [premature]
a pragmatic view: look for a set among the Sivers scan able to describe the data
we found more than one...and we computed its statistical error band

TMD phenomenology and AN in pp collisions 22

SLIDE 24

U. D’Alesio

Fermilab - 21 May 2013

Results II

Sivers contribution

0.2
0.1

0.1 0.2 0.2 0.3 0.4 AN xF θ = 2.3° π+ π− 0.1 0.2 0.3 0.4 xF θ = 4.0°

stat. bands
0.05

0.05 0.1 0.15 0.2 0.4 0.6 AN xF η = 3.3 π0 0.2 0.4 0.6 xF η = 3.7

stat. bands

BRAHMS@RHIC 2007 √s = 200 GeV STAR@RHIC 2008 Best fit and statistical error band An what about the latest flat STAR SSA data at 500 GeV and very large PT?

TMD phenomenology and AN in pp collisions 23

SLIDE 25

U. D’Alesio

Fermilab - 21 May 2013

0.05 0.1 2 3 4 5 6 7 8 AN PT (GeV) SIVERS effect STAR preliminary xF = 0.20

stat. band

70 mrad 30 mrad 0.05 0.1 2 3 4 5 6 7 8 AN PT (GeV) SIVERS effect STAR preliminary xF = 0.28

stat. band

70 mrad 30 mrad

Smaller but compatible trend

TMD phenomenology and AN in pp collisions 24

SLIDE 26

U. D’Alesio

Fermilab - 21 May 2013

0.05 0.1 2 3 4 5 6 7 8 AN PT (GeV) SIVERS effect STAR preliminary xF = 0.20

stat. band

70 mrad 30 mrad 0.05 0.1 2 3 4 5 6 7 8 AN PT (GeV) COLLINS effect STAR preliminary xF = 0.20

stat. band

70 mrad 30 mrad 0.05 0.1 2 3 4 5 6 7 8 AN PT (GeV) SIVERS effect STAR preliminary xF = 0.28

stat. band

70 mrad 30 mrad 0.05 0.1 2 3 4 5 6 7 8 AN PT (GeV) COLLINS effect STAR preliminary xF = 0.28

stat. band

70 mrad 30 mrad

Smaller but compatible trend...same for the Collins effect Caution! large PT: evolution? larger ⟨k2

⊥⟩?...further study needed!

TMD phenomenology and AN in pp collisions 25

SLIDE 27

U. D’Alesio

Fermilab - 21 May 2013

Access to the Sivers effect: pp → jet X and pp → γ X

in a TMD approach only the Sivers effect could play a role
predictions (from the optimal Sivers function set)

[Anselmino et al. 13]

0.02
0.01

0.01 0.02 0.03 0.04 0.05 0.2 0.4 0.6 AN xF √s = 500 GeV η = 3.25 pp → jet X

stat. band

ANDY data 0.02 0.04 0.06 0.08 0.1 0.2 0.4 0.6 0.8 AN xF pp → γ X √s = 200 GeV η = 3.5

stat. band

pp → jet X - ANDY data pp → γ X

TMD phenomenology and AN in pp collisions 26

SLIDE 28

U. D’Alesio

Fermilab - 21 May 2013

Access to the Sivers effect: pp → jet X and pp → γ X

comparison between TMD and (indirect) Twist-3 calculations
indication of a process dependence ???
0.02
0.01

0.01 0.02 0.03 0.04 0.05 0.2 0.4 0.6 AN xF √s = 500 GeV η = 3.25 pp → jet X

stat. band

ANDY data

N

A

F

x

0.1 0.2 0.3 0.4 0.5 0.6 −0.015 −0.01 −0.005 0.005 0.01 0.015

Sivers effect Twist-3 with TF from SIDIS [Anselmino et al. 13] [Gamberg-Kang-Prokudin 13] Notice: Sivers effect: stat. band; Twist-3 calculation: scan band

TMD phenomenology and AN in pp collisions 27

SLIDE 29

U. D’Alesio

Fermilab - 21 May 2013

Access to the Collins effect: pp → jet π X

◮ AN ∼ · · · + ∆Tq ⊗ ∆NDπ/q↑ sin(φS − φH

π )

azimuthal distribution of pions inside a jet [Yuan 08, UD-Murgia-Pisano 11] At variance with the inclusive process pp → πX, here TMD effects ARE separable (like SIDIS)

Xcm xj

zj

j

k

k k

SA

H

A

c

j

Ycm yj B Zcm

0.2
0.15
0.1
0.05

0.05 0.1 0.15 0.2 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5

p (GeV)

jT

AN

sin(φSA− φH

π )

ηj = 3.3 ≈ 0.3 ← xF

0.2
0.15
0.1
0.05

0.05 0.1 0.15 0.2 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5

p (GeV)

jT

AN

sin(φSA− φH

π )

ηj = 3.3 ≈ 0.3 ← xF π+

0.2
0.15
0.1
0.05

0.05 0.1 0.15 0.2 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5

p (GeV)

jT

AN

sin(φSA− φH

π )

ηj = 3.3 ≈ 0.3 ← xF π0

0.2
0.15
0.1
0.05

0.05 0.1 0.15 0.2 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5

p (GeV)

jT

AN

sin(φSA− φH

π )

ηj = 3.3 ≈ 0.3 ← xF π−

0.06
0.04
0.02

0.02 0.04 0.06 π π/2 3π/4 π/2 π/4

φπ

H

AN

Collins π+ π0 π-

0.06
0.04
0.02

0.02 0.04 0.06 π π/2 3π/4 π/2 π/4

φπ

H

AN

Collins π+ π0 π-

0.06
0.04
0.02

0.02 0.04 0.06 π π/2 3π/4 π/2 π/4

φπ

H

AN

Collins π+ π0 π-

0.06
0.04
0.02

0.02 0.04 0.06 π π/2 3π/4 π/2 π/4

φπ

H

AN

Collins π+ π0 π-

strong cancelation for π0 SSA (consistent with preliminary STAR data)

TMD phenomenology and AN in pp collisions 28

SLIDE 30

U. D’Alesio

Fermilab - 21 May 2013

AN at midrapidity: the gluon Sivers function

in a TMD approach for pp → π X

only the Sivers effect and gluon (sea quark) contr.s could play a role

→ constraint on the gluon Sivers function [Anselmino-UD-Melis-Murgia 06] Strategy:

use of PHENIX data [Adler et al. 05]
no information on the sea quark contribution: saturated to their bounds
0.2
0.1

0.1 0.2 1 2 3 4 5 6 AN pT (GeV/c) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.001 0.01 0.1 1 |∆Nfg(x)|/2fg(x) x

TMD phenomenology and AN in pp collisions 29

SLIDE 31

U. D’Alesio

Fermilab - 21 May 2013

Updated analysis [preliminary]

[UD-Murgia-Pisano 13]

use of new PHENIX data on π0

[Koster PhD thesis 10]

0.03
0.02
0.01

0.01 0.02 0.03 0.04 1 2 3 4 5 6 7 8 9 10 AN PT (GeV) PHENIX preliminary

AN compatible with zero:

No valence quark contribution
if no sea quark contr. →

vanishing gluon Sivers funct. (node?) A more conservative strategy: let’s focus on the small pT region (small errors)

TMD phenomenology and AN in pp collisions 30

SLIDE 32

U. D’Alesio

Fermilab - 21 May 2013

Updated analysis [preliminary]

[UD-Murgia-Pisano 13]

use of information on the sea quark contr.n (stat. band from SIDIS)
new upper bound for the gluon Sivers function (≃ one-σ)
0.002
0.001

0.001 0.002 0.003 0.004 1 1.5 2 2.5 3 3.5 4 4.5 5 AN PT (GeV) gluon total quark 0.2 0.4 0.6 0.8 1 0.001 0.01 0.1 1 Ng(x) x new bound PRD74

AN(pp → π0 X) ∆Nfg/p↑/2fg/p

TMD phenomenology and AN in pp collisions 31

SLIDE 33

U. D’Alesio

Fermilab - 21 May 2013

Updated analysis [preliminary]

[UD-Murgia-Pisano 13]

use of information on the sea quark contr.n (stat. band from SIDIS)
new upper bound for the gluon Sivers function (≃ one-σ)
0.002
0.001

0.001 0.002 0.003 0.004 1 1.5 2 2.5 3 3.5 4 4.5 5 AN PT (GeV) gluon total quark 0.001 0.01 0.1 1 10 100 0.001 0.01 0.1 1 x∆Nfg(x) x new bound PRD74 2xfg/p (GRV98)

AN(pp → π0 X) ∆Nfg/p↑ vs. 2fg/p

TMD phenomenology and AN in pp collisions 32

SLIDE 34

U. D’Alesio

Fermilab - 21 May 2013

Conclusions

SSAs in pp → hX: still challenging from the phenom. point of view
TMD and twist-3 approaches: both need further attention and work
Study of AN within a TMD scheme (assuming universality)

– two effects could play a role in pp → hX: the Collins and the Sivers effects – careful use of the information from SIDIS data unconstrained large x region

1. the Collins effect: ok ONLY at low xF
2. the Sivers effect: ok over the most pion data in size and sign
3. pp → jet(γ) X: access to the Sivers effect and disentangling approaches
4. pp → jet π X: access the Collins effect in pp collisions
AN in pp → π X at midrapidity: access to the gluon Sivers function

TMD phenomenology and AN in pp collisions 33

SLIDE 35

U. D’Alesio

Fermilab - 21 May 2013

Back-up slides

TMD phenomenology and AN in pp collisions 34

SLIDE 36

U. D’Alesio

Fermilab - 21 May 2013

Collins effect: scan band

0.05

0.05 0.1 1 1.5 2 2.5 3 3.5 AN PT (GeV) xF = 0.28 π0 1 1.5 2 2.5 3 3.5 PT (GeV) xF = 0.37

0.05

0.05 0.1 0.15 1 1.5 2 2.5 3 3.5 AN PT (GeV) xF = 0.43 π0 1 1.5 2 2.5 3 3.5 PT (GeV) xF = 0.50

STAR@RHIC: AN vs. pT for different xF bins at √s = 200 GeV

TMD phenomenology and AN in pp collisions 35

SLIDE 37

U. D’Alesio

Fermilab - 21 May 2013

Sivers effect: statistical band

0.1
0.05

0.05 0.1 0.15 1.5 2 2.5 3 3.5 AN PT (GeV) xF = 0.28 π0 1.5 2 2.5 3 3.5 PT (GeV)

stat. bands

xF = 0.37

0.1
0.05

0.05 0.1 0.15 1.5 2 2.5 3 3.5 AN PT (GeV) xF = 0.43 π0 1.5 2 2.5 3 3.5 PT (GeV)

stat. bands

xF = 0.50

STAR@RHIC: AN vs. pT for different xF bins at √s = 200 GeV

TMD phenomenology and AN in pp collisions 36

SLIDE 38

U. D’Alesio

Fermilab - 21 May 2013

Sivers effect: pp → K± X

0.05

0.05 0.1 0.2 0.3 0.4 AN xF θ = 2.3° K+ 0.2 0.3 0.4 xF K-

0.05

0.05 0.1 0.2 0.3 0.4 AN xF θ = 2.3° K+ 0.2 0.3 0.4 xF

stat. bands

K-

scan bands statistical error bands BRAHMS@RHIC: AN vs. xF

TMD phenomenology and AN in pp collisions 37

SLIDE 39

U. D’Alesio

Fermilab - 21 May 2013

Flavour dependence

hd

1 < 0 and ∆NDunf < 0 :

AN(π+) ∼ hu

1∆NDfav + hd 1∆NDunf = hu 1∆NDfav+|hd 1||∆NDunf| > 0

AN(π−) ∼ hu

1∆NDunf + hd 1∆NDfav = −hu 1|∆NDunf|−|hd 1|∆NDfav < 0

AN(π0) ∼ (hu

1 + hd 1)1

2 [ ∆NDfav + ∆NDunf ] = [ hu

1−|hd 1|

] 1 2 [ ∆NDfav−|∆NDunf| ]

up and down terms add in sign in AN(π±) while
cancel each other in AN(π0)

Notice: if ∆NDunf ≃ −∆NDfav ⇒ ACollins

N

(π0) ≃ 0

TMD phenomenology and AN in pp collisions 38

SLIDE 40

U. D’Alesio

Fermilab - 21 May 2013

)

S

φ +

h

φ sin ( UT

A

)

S

φ +

h

φ sin ( UT

A

)

S

φ +

h

φ sin ( UT

A

x z (GeV)

T

P

−0.1 0.1

π

0.05 0.1

+

π

0.1 0.2 0.3 0.4 0.5 0.6 −0.1 −0.05

−

π

−0.1

HERMES preliminary

0.2 0.4 0.6 0.8 −0.1 −0.05

−0.1

2002−2005

0.2 0.4 0.6 0.8 1 −0.1 −0.05

fit to HERMES data and statistical uncertainty band [Anselmino et al. 09]

TMD phenomenology and AN in pp collisions 39

SLIDE 41

U. D’Alesio

Fermilab - 21 May 2013

Statistical error band

χ2 =

N

∑

i=1

(yi − F (xi; a) σi )2

N measurements yi at known points xi, with variance σ2

i .

F (xi; a) depends non-linearly on M unknown parameters ai.
Best fit: χ2

min → a0

Error band: all sets of parameters such that χ2(aj) ≤ χ2

min+∆χ2

∆χ2 = 1 ↔ 1-σ: small errors, uncorrelated parameters, linearity, χ2 parabolic
∆χ2: fixed according to the coverage probability

P = ∫ ∆χ2 1 2Γ(M/2) ( χ2 2 )(M/2)−1 exp ( −χ2 2 ) dχ2 P = probability that true set of parameters falls inside the M-hypervolume [P = 0.68 ↔ 1-σ, P = 0.95 ↔ 2-σ]

TMD phenomenology and AN in pp collisions 40